A second-order accurate numerical method for a fractional wave equation

Authors:
William McLean;Kassem Mustapha
Affiliations:
School of Mathematics and Statistics, The University of New South Wales, 2052, Sydney, Australia;Department of Mathematical Sciences, KFUPM, 31261, Dhahran, Saudi Arabia
Venue:
Numerische Mathematik
Year:
2006

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Abstract

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k2 + h2, where k and h are the parameters for the time and space meshes, respectively.